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Monte Carlo Methods and simulation: random number generators, integration, Metropolis algorithm. Minimisation of multi-dimensional functions: direction set methods, simulated annealing. Linear algebra: Gauss-Jordan elimination, conjugate gradient. Partial Differential Equations. Static solutions/boundary value problems: direct matrix methods, relaxation methods, spectral methods. Time evolution problems: explicit and implicit schemes, stability analysis. Each section will include a range of problems from physics and applied mathematics.